US11860589B2 - Method and apparatus for tuning a regulatory controller - Google Patents
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- US11860589B2 US11860589B2 US17/141,806 US202117141806A US11860589B2 US 11860589 B2 US11860589 B2 US 11860589B2 US 202117141806 A US202117141806 A US 202117141806A US 11860589 B2 US11860589 B2 US 11860589B2
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/0205—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system
- G05B13/021—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system in which a variable is automatically adjusted to optimise the performance
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B11/00—Automatic controllers
- G05B11/01—Automatic controllers electric
- G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
- G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P.I., P.I.D.
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/0205—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system
- G05B13/024—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric not using a model or a simulator of the controlled system in which a parameter or coefficient is automatically adjusted to optimise the performance
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- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B11/00—Automatic controllers
- G05B11/01—Automatic controllers electric
- G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
Abstract
Description
A π(α,x)=r(α,x)+E{V π(y)|α,x}−V π(x)
The advantage is the expected return difference caused by one-step variation in a given policy. The instantaneous reward received at state x is denoted as r(a, x). Per the above definitions, Vπ(x) is the return when following the baseline policy π from x, whereas r(a, x)+Vπ(y) would be the return when applying action a at state x and causing the next environment state to be y. Because the next state y is a random variable due to a non-deterministic environment, it is necessary to take the conditional expectation E{Vπ(y)|a, x} instead of simply Vπ(y).
-
- If Aπ(α, x)≤0 for all α and x, then π is the optimal policy.
- If Aπ(α, x)>0, then applying α at x defines an improved policy with a better return.
The optimal policy can be found improving any initial policy iteratively gradually replacing all actions with ones which have positive (+ sign) advantage with respect to the current policy. The process terminates when the set of such actions is empty. Then the policy is optimal (i.e. no policy can gain better return on average). This policy improvement step is the core of policy iterations method.
-
- 1. The advantage function for a policy π is estimated.
- 2. A new policy is defined by replacing the previous actions with
-
- i.e. the action with maximum magnitude advantage, i.e. making the maximum positive improvement.
- 3. The
steps 1. And 2. are repeated with the updated policy if the policy changed in 2.
Rather than using the greedy approach, it has been found that a better approach is to use a non-greedy approach that attempts to optimize for a highest likelihood of producing a positive change in advantage, rather than a highest likelihood of producing a largest positive magnitude of change in advantage. Such non-greedy methods change the convergence process but the ultimate optimized policy remains basically the same.
-
- 1. Choosing a sufficiently long evaluation period to eliminate the effects of those states.
- 2. Defining the agent's action as the control law (e.g. PID gains) selection, not actuator position, to avoid irresponsiveness during the evaluation period.
-
- 1. Those RL agent's actions which are close to optimal will produce valid data.
- 2. Incorrect actions will produce low quality data which will cause problems in the algorithm.
Or possibly a soft continuous version of the sign function σ(Aπ) to avoid problems with discontinuity:
This choice still secures the convergence to the optimal policy, although the convergence rate may be slower compared to the greedy approach in ideal conditions (without outliers). At the same time, this choice is less sensitive to outliers, i.e. effects of the unknown process states.
A π(α,x)=r(α,x)+E{r(α,y)|α,x}−r(π(x),x)−E{r(π(y),y)|π(x),x}
V α(x)=r(α,x)+(π(y),y)
V π(x)=r(π(x),x)+r(π(y),y)
The average is an empirical advantage datum obtained by testing an action N times and observing the costs. Consider the actual advantage function at the current initial state is x
A π(α,x)=1−16α2
From here, the optimal action is clearly zero. Suppose the empirical advantage converges to the actual advantage for N→∞ but the rate of convergence is much slower for suboptimal actions. This represents a similar mechanism like the regulatory control instability: it is much harder to determine the actual advantage or actual disadvantage for the suboptimal destabilizing controllers because these will be very sensitive to the intermediate states as well to the process nonlinearities and other complex effects.
-
- 1. Tuning values αi
- 2. Initial process state xi
- 3. Aggregated loss ri
- 4. Terminal process state yi
r i(t+1)=r i(t)−(y cv(t)−y sp(t))2−ρ(u mv(t)−u mv(t−1))2,
where ycv(t), ysp(t) are the controlled variable and its set-point respectively and umv(t) is the manipulated variable (controller output) at time t. The non-negative p is a tuning parameter used to define the optimal speed of response.
A i 0 =r i +V 0(y i)−V 0(x i)
Positive Ai indicate evaluation periods during which the edge device performed above average and vice versa. The algorithm uses such data to classify the actions (tuning vectors) into two classes: above average (or average at worst) Ai 0≥0 and below average Ai 0<0. This classification is in fact a model of the Ai 0 sign. The tuning values which performed below average can now be rejected and eliminated from the data. In the next iteration, the improved cost-to-go can be calculated V1(x) not accounting for the rejected evaluation periods. The further improvement is achieved classifying the perturbations into below versus above average with respect to V1(x) using the refined advantage values Ai 1. This process finally converges to an Ai n after n iterations presumably approximating the advantage function of the optimal policy, i.e. Ai n≥0. It can be noted that while the advantage values are calculated even for eliminated periods at every iteration, the elimination concerns only the cost-to-go calculations.
This method would produce a controller tuning of which depends on the process state. However, simple controllers like PID are more frequently described by tuning values which are constant, independent on the process state. This can be overcome by eliminating the state x, e.g. averaging it:
In this way, the tuning vector which performs optimally on average is preferred instead of a state—dependent optimal tuning. Sometimes, the tuning dependency on the state may be desirable. Finally, the above calculated a* representing an improved controller tuning vector is sent back to the edge device. There, it replaces the current values and the edge device starts applying it including the randomized perturbations. This process may be repeated going forward. In this way, the controller tuning is permanently adapting to the changing environment.
Claims (18)
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US17/141,806 US11860589B2 (en) | 2021-01-05 | 2021-01-05 | Method and apparatus for tuning a regulatory controller |
EP21217649.9A EP4024143A1 (en) | 2021-01-05 | 2021-12-23 | Method and apparatus for tuning a regulatory controller |
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